Linearization of analytic order relations
Abstract
We prove that if $\leq$ is an analytic partial order then either $\leq$ can be extended to a (boldface) $\Delta^1_2$ linear order similar to an antichain in $2^{<\omega_1}$ ordered lexicographically or a certain Borel partial order $\leq_0$ embeds in $\leq.$ Some corollaries for analytic equivalence relations are given, for instance, if $E$ is a $\Sigma^1_1[z]$ equivalence relation such that $E_0$ does not embed in $E$ then $E$ is determined by intersections with E-invariand Borel sets coded in $L[z]$.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- June 1997
- DOI:
- 10.48550/arXiv.math/9706204
- arXiv:
- arXiv:math/9706204
- Bibcode:
- 1997math......6204K
- Keywords:
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- Mathematics - Logic
- E-Print:
- Annals of Pure and Applied Logic, 2000, 102, 1-2, pp. 69-100